The minimum value of 27cos2x 81sin2x is from Math

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 Multiple Choice QuestionsMultiple Choice Questions

241.

The point on the curve y2 = x the tangent at which makes an angle 45° with X-axis ts

  • 14, 12

  • 12, 14

  • 12, - 12

  • 12, 12


242.

The length of the subtangent to the curve x2y2 = a4 at (- a, a)

  • a2

  • 2a

  • a

  • a3


243.

A stone is thrown vertically upwards and the height x ft reached by the stone in t seconds is given by x = 80 t - 16t2 The stone reaches the maximum height in

  • 2 s

  • 2.5 s

  • 3 s

  • 1.5 s


244.

The maximum value of logxx in 2,  is

  • 1

  • 2e

  • e

  • 1e


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245.

The tangent to a given curve y = f(x) is perpendicular to the x-axis, if

  • dydx - 1

  • dxdy = 0

  • dxdy = 1

  • dydx = 0


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246.

The minimum value of 27cos2x 81sin2x is

  • - 5

  • 15

  • 1243

  • 127


C.

1243

Let fx = 27cos2x 81sin2x            = 33cos3x + 4sin2xLet   35 = sinϕ  45 = cosϕthen fx = 35sinϕcos2x + cosϕsin2x              = 35sinϕ +2xFor minimum value of given function,sinϕ +2x will be minimum.i.e., sinϕ +2x = - 1 fx = 35- 1           = 1243


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247.

A stone is thrown vertically upwards from the top of a tower 64 m high according to the law s = 48t - 16t2. The greatest height attained by the stone above ground is

  • 36 m

  • 32 m

  • 100  m

  • 64 m


248.

The length of the subtangent at t on the curve x = at + sint, y = a1 - cost

  • asint

  • 2asint2tant2

  • 2asint2

  • 2asin3t2sect2


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249.

A wire of length 20 cm is bent in the form of a sector of a circle. The maximum area that can be enclosed by the wire is

  • 20 sq cm

  • 25 sq cm

  • 10 sq cm

  • 30 sq cm


250.

The condition for the line y = mx + c to be a normal to the parabola y2 = 4ax is

  • c = - 2am - am3

  • c = - am

  • c = am

  • c = 2am + am3


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